The denial of actualism is possibilism, the thesis that there are some entities that are merely possible: these entities have being but are not actual and, hence, enjoy a "less robust" sort of being than do actually existing things. An important, but significantly different notion of possibilism known as modal realism was developed by the philosopher David Lewis.[1] On Lewis's account, the actual world is identified with the physical universe of which we are all a part. Other possible worlds exist in exactly the same sense as the actual world; they are simply spatio-temporally unrelated to our world, and to each other. Hence, for Lewis, "merely possible" entities—entities that exist in other possible worlds—exist in exactly the same sense as do we in the actual world; to be actual, from the perspective of any given individual x in any possible world, is simply to be part of the same world as x.

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Consider the statement "Sherlock Holmes exists." This is a false statement about the world, but is usually accepted as representing a possible truth. This contingency is usually described by the statement "there is a possible world in which Sherlock Holmes exists". The possibilist argues that apparent existential claims such as this (that "there are" possible worlds of various sorts) ought to be taken more or less at face value: as stating the existence of two or more worlds, only one of which (at the most) can be the actual one. Hence, they argue, there are innumerably many possible worlds other than our own, which exist just as much as ours does.

Most actualists will be happy to grant the interpretation of "Sherlock Holmes' existence is possible" in terms of possible worlds. But they argue that the possibilist goes wrong in taking this as a sign that there exist other worlds that are just like ours, except for the fact that we are not actually in them. The actualist argues, instead, that when we claim "possible worlds" exist we are making claims that things exist in our own actual world which can serve as possible worlds for the interpretation of modal claims: that many ways the world could be (actually) exist, but not that any worlds which are those ways exist other than the actual world around us.

From an actualist point of view, such as Adams', possible worlds are nothing more than fictions created within the actual world. Possible worlds are mere descriptions of ways this world (the actual one) might have been, and nothing else. Thus, as modal constructions, they come in as a handy heuristic device to use with modal logic; as it helps our modal reasoning to imagine ways the world might have been. Thus, the actualist interpretation of "◊p" sees the modality (i.e., "the way" in which it is true) as being de dicto and not entailing any ontological commitment.

So, from this point of view, what distinguishes the actual world from other possible worlds is what distinguishes reality from a description of a simulation of reality, this world from Sherlock Holmes': the former exists and is not a product of imagination and the latter does not exist and is a product of the imagination set in a modal construction.[4]

From a modal realist’s point of view, such as Lewis', the proposition "◊p" means that p obtains in at least one other, distinct world that is as real as the one we are in. If a state of affairs is possible, then it really obtains, it physically occurs in at least one world. Therefore, as Lewis is happy to admit, there is a world where someone named Sherlock Holmes lived at 221b Baker Street in Victorian times, there is another world where pigs fly, and there is even another world where both Sherlock Holmes exists and pigs fly.[5]

This leaves open the question, of course, of what an actually existing "way the world could be" is; and on this question actualists are divided. One of the most popular solutions is to claim, as William Lycan and Robert Adams do, that "possible worlds" talk can be reduced to logical relations amongst consistent and maximally complete sets of propositions. "Consistent" here means that none of its propositions contradict one another (if they did, it would not be a possible description of the world); "maximally complete" means that the set covers every feature of the world. (More precisely: a set of propositions is "maximally complete" if, for any meaningful proposition P, P is either an element of the set, or the negation of an element of the set, or entailed by the conjunction of one or more elements of the set, or the negation of a proposition entailed by the conjunction of one or more elements of the set). Here the "possible world" which is said to be actual is actual in virtue of all its elements being true of the world around us.

Another common actualist account, advanced in different forms by Alvin Plantinga and David Armstrong views "possible worlds" not as descriptions of how the world might be (through a very large set of statements) but rather as a maximally complete state of affairs that covers every state of affairs which might obtain or not obtain. Here, the "possible world" which is said to be actual is actual in virtue of that state of affairs obtaining in the world around us. (Since it is maximally complete, only one such state of affairs could actually obtain; all the others would differ from the actual world in various large or small ways.)

According to the indexical conception of actuality, favoured by Lewis (1986), actuality is an attribute which our world has relative to itself, but which all the other worlds have relative to themselves too. Actuality is an intrinsic property of each world, so world w is actual just at world w. "Actual" is seen as an indexical term, and its reference depends on its context.[6] Therefore, there is no feature of this world (nor of any other) to be distinguished in order to infer that the world is actual, "the actual world" is actual simply in virtue of the definition of "actual": a world is actual simpliciter.

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